Fourier: Making Waves

Fourier: Making Waves Screenshot
  • Waves
  • Sines
  • Cosines
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Topics

  • Waves
  • Sines
  • Cosines

Description

Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.

Sample Learning Goals

  • Explain qualitatively how sines and cosines add up to produce arbitrary periodic functions.
  • Recognize that each Fourier component corresponds to a sinusoidal wave with a different wavelength or period.
  • Mentally map simple functions between Fourier space and real space.
  • Describe sounds in terms of sinusoidal waves.
  • Describe the difference between waves in space and waves in time.
  • Recognize that wavelength and period do not correspond to specific points on the graph but indicate the length/time between two consecutive troughs, peaks, or any other corresponding points.
  • Become comfortable with various mathematical notations for writing Fourier transforms, and relate the mathematics to an intuitive picture of wave forms.
  • Determine which aspect of a graph of a wave is described by each of the symbols lambda, T, k, omega, and n.
  • Recognize that lambda & T and k & omega are analogous, but not the same.
  • Translate an equation from summation notation to extended notation.
  • Recognize that the width of a wave packet in position space is inversely related to the width of a wave packet in Fourier space.
  • Explain how the Heisenberg Uncertainty principle results from the properties of waves.
  • Recognize that the spacing between Fourier components is inversely related to the spacing between wave packets, and that a continuous distribution of fourier components leads to a single wave packet.
Version 3.06

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Concept questions for Physics using PhET (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
MC Physics
Algebra-based Physics Semester one lessons, clicker questions, and schedule in pdf (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Lab
Demo
HW
Physics
Wave unit (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Demo
Lab
Physics
Wave clicker questions (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
CQs Physics
Waves: Superposition (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
CQs
Lab
Mathematics
Physics
Wave Representations (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Lab Physics
Fourier Making Waves Game (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS Lab Physics
Wave Modeling and Wave addition (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
Lab Physics
How do PhET simulations fit in my middle school program? This contribution was designed by PhET. Sarah Borenstein MS Other Earth Science
Chemistry
Biology
Physics
Introduction to Fourier Analysis This contribution was designed by PhET. Sam McKagan, Kathy Perkins and Carl Wieman UG-Adv
UG-Intro
HW Physics
Mathematics
Mapping of PhET and IBDP Physics Jaya Ramchandani HS Other Physics
MS and HS TEK to Sim Alignment Elyse Zimmer MS
HS
Other Biology
Chemistry
Physics
Making use of the Sound Simulations Don Cameron HS Lab Physics

Language Download or Run Tips
Amharic All Amharic Run now አራትዮሽ፡ ሞገድ መስራት
Basque All Euskara Run now Fourier: Uhinak sortzen
Bosnian All Bosanski Run now FURIJE-OVA SINTEZA - PRAVLJENJE TALASA
Bulgarian All български Run now Фурие: Получаване на вълни
Chinese (Simplified) All 中文 (中国) Run now 傅里叶:生成波
Chinese (Traditional) All 中文 (台灣) Run now Fourier: Making Waves 傅力葉:與波共舞
Croatian All hrvatski Run now Kompozicija valova (Fourierova sinteza)
Danish All Dansk Run now Fourir: Bølgefremstilling
Dutch All Nederlands Run now Boventonen
Estonian All Eesti Run now Fourier: Lainete tekitamine
French All français Run now Fourier: Création d'ondes
German All Deutsch Run now Wellen zusammensetzen nach FOURIER
Greek All Ελληνικά Run now Fourier: Δημιουργία Κυμάτων
Hebrew All עברית Run now פוריה: עושים גלים
Hungarian All magyar Run now Fourier: hullám-LEGO
Indonesian All Bahasa Indonesia Run now Fourier : Mengkontruksi Gelombang
Italian All italiano Run now Fourier: Costruire le onde
Japanese All 日本語 Run now フーリエ級数展開:波の合成
Khmer All Khmer Run now Fourier: ការបង្កើតរលក
Korean All 한국어 Run now 푸리에: 파동 생성
Lao All Lao Run now ຟູເຍ້: ການເຮັດໃຫ້ຄື້ນຟອງ
Macedonian All македонски Run now ФУРИОВА СИНТЕЗА -ПРАВЕЊЕ НА БРАНОВИ
Mongolian All Монгол (Монгол) Run now Фурьей: Долгион хийх
Persian All فارسی Run now تولید موج ها
Polish All polski Run now Fourier: Konstruowanie fal
Portuguese All português Run now Séries de Fourier: Fazendo Ondas
Portuguese (Brazil) All português (Brasil) Run now Fourier: Criando Ondas
Serbian All Српски Run now ФУРИЈЕ-ОВА СИНТЕЗА -ПРАВЉЕЊЕ ТАЛАСА
Slovak All Slovenčina Run now Fourier: tvorenie vĺn
Spanish All español Run now Fourier: Fabricacion de Ondas Download teacher tips PDF
Spanish (Mexico) All español (México) Run now Fourier: Fabricacion de Ondas Download teacher tips PDF
Spanish (Peru) All español (Perú) Run now Fourier: Haciendo Ondas
Turkish All Türkçe Run now Fourier Serileri: Dalga Yapalım
Turkmen All Turkmen Run now Furýe: tolkun ýasamak
Vietnamese All Tiếng Việt Run now Tổng hợp sóng

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Design Team Third-party Libraries Thanks To
  • Chris Malley (developer)
  • Sam McKagan (lead)
  • Carl Wieman
  • Interviewer: Danielle Harlow
  • Interviewer: Sam McKagan